{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第6章 逻辑斯谛回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "逻辑斯谛回归(LR)是经典的分类方法\n",
    "\n",
    "1．逻辑斯谛回归模型是由以下条件概率分布表示的分类模型。逻辑斯谛回归模型可以用于二类或多类分类。\n",
    "\n",
    "$$P(Y=k | x)=\\frac{\\exp \\left(w_{k} \\cdot x\\right)}{1+\\sum_{k=1}^{K-1} \\exp \\left(w_{k} \\cdot x\\right)}, \\quad k=1,2, \\cdots, K-1$$\n",
    "\n",
    "$$P(Y=K | x)=\\frac{1}{1+\\sum_{k=1}^{K-1} \\exp \\left(w_{k} \\cdot x\\right)}$$\n",
    "这里，$x$为输入特征，$w$为特征的权值。\n",
    "\n",
    "逻辑斯谛回归模型源自逻辑斯谛分布，其分布函数$F(x)$是$S$形函数。逻辑斯谛回归模型是由输入的线性函数表示的输出的对数几率模型。\n",
    "\n",
    "2．最大熵模型是由以下条件概率分布表示的分类模型。最大熵模型也可以用于二类或多类分类。\n",
    "\n",
    "$$P_{w}(y | x)=\\frac{1}{Z_{w}(x)} \\exp \\left(\\sum_{i=1}^{n} w_{i} f_{i}(x, y)\\right)$$\n",
    "$$Z_{w}(x)=\\sum_{y} \\exp \\left(\\sum_{i=1}^{n} w_{i} f_{i}(x, y)\\right)$$\n",
    "\n",
    "其中，$Z_w(x)$是规范化因子，$f_i$为特征函数，$w_i$为特征的权值。\n",
    "\n",
    "3．最大熵模型可以由最大熵原理推导得出。最大熵原理是概率模型学习或估计的一个准则。最大熵原理认为在所有可能的概率模型（分布）的集合中，熵最大的模型是最好的模型。\n",
    "\n",
    "最大熵原理应用到分类模型的学习中，有以下约束最优化问题：\n",
    "\n",
    "$$\\min -H(P)=\\sum_{x, y} \\tilde{P}(x) P(y | x) \\log P(y | x)$$\n",
    "\n",
    "$$s.t.  \\quad P\\left(f_{i}\\right)-\\tilde{P}\\left(f_{i}\\right)=0, \\quad i=1,2, \\cdots, n$$\n",
    " \n",
    " $$\\sum_{y} P(y | x)=1$$\n",
    " \n",
    "求解此最优化问题的对偶问题得到最大熵模型。\n",
    "\n",
    "4．逻辑斯谛回归模型与最大熵模型都属于对数线性模型。\n",
    "\n",
    "5．逻辑斯谛回归模型及最大熵模型学习一般采用极大似然估计，或正则化的极大似然估计。逻辑斯谛回归模型及最大熵模型学习可以形式化为无约束最优化问题。求解该最优化问题的算法有改进的迭代尺度法、梯度下降法、拟牛顿法。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "回归模型：$f(x) = \\frac{1}{1+e^{-wx}}$\n",
    "\n",
    "其中wx线性函数：$wx =w_0\\cdot x_0 + w_1\\cdot x_1 + w_2\\cdot x_2 +...+w_n\\cdot x_n,(x_0=1)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import exp\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data\n",
    "def create_data():\n",
    "    iris = load_iris()\n",
    "    df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "    df['label'] = iris.target\n",
    "    df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']\n",
    "    data = np.array(df.iloc[:100, [0,1,-1]])\n",
    "    # print(data)\n",
    "    return data[:,:2], data[:,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = create_data()\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LogisticReressionClassifier:\n",
    "    def __init__(self, max_iter=200, learning_rate=0.01):\n",
    "        self.max_iter = max_iter\n",
    "        self.learning_rate = learning_rate\n",
    "\n",
    "    def sigmoid(self, x):\n",
    "        return 1 / (1 + exp(-x))\n",
    "\n",
    "    def data_matrix(self, X):\n",
    "        data_mat = []\n",
    "        for d in X:\n",
    "            data_mat.append([1.0, *d])\n",
    "        return data_mat\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        # label = np.mat(y)\n",
    "        data_mat = self.data_matrix(X)  # m*n\n",
    "        self.weights = np.zeros((len(data_mat[0]), 1), dtype=np.float32)\n",
    "\n",
    "        for iter_ in range(self.max_iter):\n",
    "            for i in range(len(X)):\n",
    "                result = self.sigmoid(np.dot(data_mat[i], self.weights))\n",
    "                error = y[i] - result\n",
    "                self.weights += self.learning_rate * error * np.transpose(\n",
    "                    [data_mat[i]])\n",
    "        print('LogisticRegression Model(learning_rate={},max_iter={})'.format(\n",
    "            self.learning_rate, self.max_iter))\n",
    "\n",
    "    # def f(self, x):\n",
    "    #     return -(self.weights[0] + self.weights[1] * x) / self.weights[2]\n",
    "\n",
    "    def score(self, X_test, y_test):\n",
    "        right = 0\n",
    "        X_test = self.data_matrix(X_test)\n",
    "        for x, y in zip(X_test, y_test):\n",
    "            result = np.dot(x, self.weights)\n",
    "            if (result > 0 and y == 1) or (result < 0 and y == 0):\n",
    "                right += 1\n",
    "        return right / len(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression Model(learning_rate=0.01,max_iter=200)\n"
     ]
    }
   ],
   "source": [
    "lr_clf = LogisticReressionClassifier()\n",
    "lr_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b6e7cc16c8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_ponits = np.arange(4, 8)\n",
    "y_ = -(lr_clf.weights[1]*x_ponits + lr_clf.weights[0])/lr_clf.weights[2]\n",
    "plt.plot(x_ponits, y_)\n",
    "\n",
    "#lr_clf.show_graph()\n",
    "plt.scatter(X[:50,0],X[:50,1], label='0')\n",
    "plt.scatter(X[50:,0],X[50:,1], label='1')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### scikit-learn实例\n",
    "\n",
    "#### sklearn.linear_model.LogisticRegression\n",
    "\n",
    "solver参数决定了我们对逻辑回归损失函数的优化方法，有四种算法可以选择，分别是：\n",
    "- a) liblinear：使用了开源的liblinear库实现，内部使用了坐标轴下降法来迭代优化损失函数。\n",
    "- b) lbfgs：拟牛顿法的一种，利用损失函数二阶导数矩阵即海森矩阵来迭代优化损失函数。\n",
    "- c) newton-cg：也是牛顿法家族的一种，利用损失函数二阶导数矩阵即海森矩阵来迭代优化损失函数。\n",
    "- d) sag：即随机平均梯度下降，是梯度下降法的变种，和普通梯度下降法的区别是每次迭代仅仅用一部分的样本来计算梯度，适合于样本数据多的时候。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = LogisticRegression(max_iter=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(max_iter=200)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.59546005 -2.81261232]] [-5.08164524]\n"
     ]
    }
   ],
   "source": [
    "print(clf.coef_, clf.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b6e8248fc8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_ponits = np.arange(4, 8)\n",
    "y_ = -(clf.coef_[0][0]*x_ponits + clf.intercept_)/clf.coef_[0][1]\n",
    "plt.plot(x_ponits, y_)\n",
    "\n",
    "plt.plot(X[:50, 0], X[:50, 1], 'bo', color='blue', label='0')\n",
    "plt.plot(X[50:, 0], X[50:, 1], 'bo', color='orange', label='1')\n",
    "plt.xlabel('sepal length')\n",
    "plt.ylabel('sepal width')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 最大熵模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "from copy import deepcopy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MaxEntropy:\n",
    "    def __init__(self, EPS=0.005):\n",
    "        self._samples = []\n",
    "        self._Y = set()  # 标签集合，相当去去重后的y\n",
    "        self._numXY = {}  # key为(x,y)，value为出现次数\n",
    "        self._N = 0  # 样本数\n",
    "        self._Ep_ = []  # 样本分布的特征期望值\n",
    "        self._xyID = {}  # key记录(x,y),value记录id号\n",
    "        self._n = 0  # 特征键值(x,y)的个数\n",
    "        self._C = 0  # 最大特征数\n",
    "        self._IDxy = {}  # key为(x,y)，value为对应的id号\n",
    "        self._w = []\n",
    "        self._EPS = EPS  # 收敛条件\n",
    "        self._lastw = []  # 上一次w参数值\n",
    "\n",
    "    def loadData(self, dataset):\n",
    "        self._samples = deepcopy(dataset)\n",
    "        for items in self._samples:\n",
    "            y = items[0]\n",
    "            X = items[1:]\n",
    "            self._Y.add(y)  # 集合中y若已存在则会自动忽略\n",
    "            for x in X:\n",
    "                if (x, y) in self._numXY:\n",
    "                    self._numXY[(x, y)] += 1\n",
    "                else:\n",
    "                    self._numXY[(x, y)] = 1\n",
    "\n",
    "        self._N = len(self._samples)\n",
    "        self._n = len(self._numXY)\n",
    "        self._C = max([len(sample) - 1 for sample in self._samples])\n",
    "        self._w = [0] * self._n\n",
    "        self._lastw = self._w[:]\n",
    "\n",
    "        self._Ep_ = [0] * self._n\n",
    "        for i, xy in enumerate(self._numXY):  # 计算特征函数fi关于经验分布的期望\n",
    "            self._Ep_[i] = self._numXY[xy] / self._N\n",
    "            self._xyID[xy] = i\n",
    "            self._IDxy[i] = xy\n",
    "\n",
    "    def _Zx(self, X):  # 计算每个Z(x)值\n",
    "        zx = 0\n",
    "        for y in self._Y:\n",
    "            ss = 0\n",
    "            for x in X:\n",
    "                if (x, y) in self._numXY:\n",
    "                    ss += self._w[self._xyID[(x, y)]]\n",
    "            zx += math.exp(ss)\n",
    "        return zx\n",
    "\n",
    "    def _model_pyx(self, y, X):  # 计算每个P(y|x)\n",
    "        zx = self._Zx(X)\n",
    "        ss = 0\n",
    "        for x in X:\n",
    "            if (x, y) in self._numXY:\n",
    "                ss += self._w[self._xyID[(x, y)]]\n",
    "        pyx = math.exp(ss) / zx\n",
    "        return pyx\n",
    "\n",
    "    def _model_ep(self, index):  # 计算特征函数fi关于模型的期望\n",
    "        x, y = self._IDxy[index]\n",
    "        ep = 0\n",
    "        for sample in self._samples:\n",
    "            if x not in sample:\n",
    "                continue\n",
    "            pyx = self._model_pyx(y, sample)\n",
    "            ep += pyx / self._N\n",
    "        return ep\n",
    "\n",
    "    def _convergence(self):  # 判断是否全部收敛\n",
    "        for last, now in zip(self._lastw, self._w):\n",
    "            if abs(last - now) >= self._EPS:\n",
    "                return False\n",
    "        return True\n",
    "\n",
    "    def predict(self, X):  # 计算预测概率\n",
    "        Z = self._Zx(X)\n",
    "        result = {}\n",
    "        for y in self._Y:\n",
    "            ss = 0\n",
    "            for x in X:\n",
    "                if (x, y) in self._numXY:\n",
    "                    ss += self._w[self._xyID[(x, y)]]\n",
    "            pyx = math.exp(ss) / Z\n",
    "            result[y] = pyx\n",
    "        return result\n",
    "\n",
    "    def train(self, maxiter=1000):  # 训练数据\n",
    "        for loop in range(maxiter):  # 最大训练次数\n",
    "            print(\"iter:%d\" % loop)\n",
    "            self._lastw = self._w[:]\n",
    "            for i in range(self._n):\n",
    "                ep = self._model_ep(i)  # 计算第i个特征的模型期望\n",
    "                self._w[i] += math.log(self._Ep_[i] / ep) / self._C  # 更新参数\n",
    "            print(\"w:\", self._w)\n",
    "            if self._convergence():  # 判断是否收敛\n",
    "                break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = [['no', 'sunny', 'hot', 'high', 'FALSE'],\n",
    "           ['no', 'sunny', 'hot', 'high', 'TRUE'],\n",
    "           ['yes', 'overcast', 'hot', 'high', 'FALSE'],\n",
    "           ['yes', 'rainy', 'mild', 'high', 'FALSE'],\n",
    "           ['yes', 'rainy', 'cool', 'normal', 'FALSE'],\n",
    "           ['no', 'rainy', 'cool', 'normal', 'TRUE'],\n",
    "           ['yes', 'overcast', 'cool', 'normal', 'TRUE'],\n",
    "           ['no', 'sunny', 'mild', 'high', 'FALSE'],\n",
    "           ['yes', 'sunny', 'cool', 'normal', 'FALSE'],\n",
    "           ['yes', 'rainy', 'mild', 'normal', 'FALSE'],\n",
    "           ['yes', 'sunny', 'mild', 'normal', 'TRUE'],\n",
    "           ['yes', 'overcast', 'mild', 'high', 'TRUE'],\n",
    "           ['yes', 'overcast', 'hot', 'normal', 'FALSE'],\n",
    "           ['no', 'rainy', 'mild', 'high', 'TRUE']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "maxent = MaxEntropy()\n",
    "x = ['overcast', 'mild', 'high', 'FALSE']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter:0\n",
      "w: [0.0455803891984887, -0.002832177999673058, 0.031103560672370825, -0.1772024616282862, -0.0037548445453157455, 0.16394435955437575, -0.02051493923938058, -0.049675901430111545, 0.08288783767234777, 0.030474400362443962, 0.05913652210443954, 0.08028783103573349, 0.1047516055195683, -0.017733409097415182, -0.12279936099838235, -0.2525211841208849, -0.033080678592754015, -0.06511302013721994, -0.08720030253991244]\n",
      "iter:1\n",
      "w: [0.11525071899801315, 0.019484939219927316, 0.07502777039579785, -0.29094979172869884, 0.023544184009850026, 0.2833018051925922, -0.04928887087664562, -0.101950931659509, 0.12655289130431963, 0.016078718904129236, 0.09710585487843026, 0.10327329399123442, 0.16183727320804359, 0.013224083490515591, -0.17018583153306513, -0.44038644519804815, -0.07026660158873668, -0.11606564516054546, -0.1711390483931799]\n",
      "iter:2\n",
      "w: [0.18178907332733973, 0.04233703122822168, 0.11301330241050131, -0.37456674484068975, 0.05599764270990431, 0.38356978711239126, -0.07488546168160945, -0.14671211613144097, 0.15633348706002106, -0.011836411721359321, 0.12895826039781944, 0.10572969681821211, 0.19953102749655352, 0.06399991656546679, -0.17475388854415905, -0.5893308194447993, -0.10405912653008922, -0.16350962040062977, -0.24701967386590512]\n",
      "iter:3\n",
      "w: [0.2402117261976856, 0.06087651054892573, 0.14300856884173724, -0.44265412294427664, 0.08623192206158618, 0.47264512563925376, -0.09600090083002198, -0.18353847640798293, 0.17967535014110475, -0.04398112111909075, 0.15854994616895085, 0.09937760679990165, 0.22754399461146121, 0.12138068016302067, -0.15616500410638443, -0.7136213594089919, -0.13342640817803014, -0.2097936229338585, -0.3153356710047331]\n",
      "iter:4\n",
      "w: [0.2914313208012359, 0.07547654306538813, 0.16668283431764536, -0.5013655616789854, 0.1129176109082406, 0.553725824276617, -0.11340104779016447, -0.214026170852028, 0.19932565541497924, -0.07698174342694904, 0.18676347888513212, 0.08897527479225055, 0.250034281885875, 0.17966909953761648, -0.12561912266368833, -0.8214131440732644, -0.15887039192864807, -0.255021849396353, -0.3775163032854775]\n",
      "iter:5\n",
      "w: [0.3371038340609469, 0.08719816942080917, 0.1858885244336221, -0.5536101929687616, 0.13629778855333752, 0.6284587190599515, -0.12800357294309486, -0.23983404211792342, 0.21652676634149073, -0.10944257416223822, 0.2137132093479417, 0.07676820672685672, 0.2690824414813502, 0.2363909590693551, -0.0894456215757756, -0.9176374337279947, -0.18113135827470755, -0.298867529863144, -0.43486330681003177]\n",
      "iter:6\n",
      "w: [0.3785824456804424, 0.09688384478129128, 0.2020182323803342, -0.6009874705178111, 0.15692184161636785, 0.6978719259357552, -0.14051015547758733, -0.26225964542470354, 0.231946295562788, -0.14075188805495795, 0.23936253047337575, 0.06390380813674021, 0.2858409112894462, 0.290497131241793, -0.05118245076440544, -1.0054122371529666, -0.20087035680546067, -0.34104258966535955, -0.4883751534969831]\n",
      "iter:7\n",
      "w: [0.41683868296814264, 0.10509553912347498, 0.2160232475329699, -0.644505058740366, 0.1753178575881968, 0.7626984543065831, -0.1514056957963993, -0.282232009175799, 0.24599431757478898, -0.17065092475910307, 0.26368621835608597, 0.0509851487070869, 0.3009923148407335, 0.3416039921608126, -0.012757343850577675, -1.0867762087449189, -0.218615635191165, -0.3813835600318599, -0.5387838195368846]\n",
      "iter:8\n",
      "w: [0.45255283727071915, 0.11219377184169538, 0.2285350985725094, -0.6848643375624139, 0.19192374296509346, 0.823505441985143, -0.1610195381343653, -0.3003952716953118, 0.2589475960707626, -0.19905447303514948, 0.28670003432375235, 0.03832451391813461, 0.3149608328705212, 0.38965093728157896, 0.024829827991967576, -1.1631007696620375, -0.234775223274346, -0.4198375433999549, -0.5866232900677824]\n",
      "iter:9\n",
      "w: [0.4862047341699185, 0.11841188281430236, 0.23997121190141055, -0.7225858897027357, 0.20708669598089463, 0.8807531715193149, -0.16957936712401173, -0.3171924798474509, 0.27100498873946605, -0.2259668872025463, 0.30845455112675946, 0.02607293739294267, 0.3280204662447941, 0.43473488104744773, 0.06110854499605007, -1.235334453720919, -0.2496614393236233, -0.4564297086590982, -0.632287633902211]\n",
      "iter:10\n",
      "w: [0.5181394259405306, 0.12390610358940803, 0.25060941880919724, -0.7580715708198793, 0.22107810865652675, 0.9348258037844982, -0.17724821171219282, -0.3329298610812439, 0.28231538356745023, -0.25143909184677066, 0.3290224934515896, 0.01429111840050851, 0.34035457030022254, 0.4770259468712468, 0.09590445328801561, -1.3041525627362545, -0.2635134591021718, -0.4912340995712618, -0.676073174743828]\n",
      "iter:11\n",
      "w: [0.5486110820346487, 0.12878621492610728, 0.260637166739537, -0.7916392134506605, 0.23410952494004347, 0.9860494937682006, -0.18414786231688304, -0.34782183358804564, 0.29299341588094513, -0.2755452075588528, 0.3484877282959149, 0.0029897746989391953, 0.3520901674994048, 0.5167232266096159, 0.12920353885993147, -1.3700506081491441, -0.2765153028028459, -0.5243519897715138, -0.7182076215567675]\n",
      "iter:12\n",
      "w: [0.5778117345209275, 0.13313363017604996, 0.27018325256816517, -0.8235442751999533, 0.24634619366524757, 1.0347042729774998, -0.19037323865834888, -0.36202132448933444, 0.3031291458576307, -0.2983694137224091, 0.36693744589848354, -0.007847001125305455, 0.36331836466580314, 0.5540314435560996, 0.16107375873385849, -1.43340343709795, -0.2888095132477581, -0.5558971523336302, -0.7588699023545793]\n",
      "iter:13\n",
      "w: [0.6058901351026187, 0.13701191167326482, 0.27933812605788444, -0.8539945297938123, 0.2579178021404349, 1.0810325152985145, -0.19600113559558124, -0.3756398474403068, 0.3127944422531689, -0.31999848717048135, 0.38445717638507615, -0.01824819811068835, 0.374106791262247, 0.5891489137038122, 0.19162049156992134, -1.494503092195292, -0.3005073854549682, -0.5859863925416857, -0.7982036819948133]\n",
      "iter:14\n",
      "w: [0.6329642597528577, 0.14047287909653053, 0.288166877587425, -0.8831606263070614, 0.2689267548911857, 1.1252453301017262, -0.2010955813068598, -0.38876072186638005, 0.32204740845586133, -0.3405176107915853, 0.40112790161689965, -0.02824811730597898, 0.38450732666115006, 0.6222617230970029, 0.22096178876573108, -1.553583366887057, -0.3116965772848507, -0.614733784830676, -0.8363266559598186]\n",
      "iter:15\n",
      "w: [0.6591297272306862, 0.14356019142928794, 0.29671758022981304, -0.9111839584847241, 0.27945449028395125, 1.1675275789036936, -0.2057111806049296, -0.40144778446237106, 0.3309355607379767, -0.3600081062970341, 0.417024586229216, -0.0378820228099265, 0.3945609896455332, 0.6535413341943247, 0.2492151298378952, -1.6108359714954945, -0.322446770130228, -0.6422474013311557, -0.8733370228190042]\n",
      "iter:16\n",
      "w: [0.6844655652033881, 0.14631149268101387, 0.3050266859363578, -0.9381826602314054, 0.28956628018821073, 1.208041909775652, -0.20989526326523208, -0.4137511617306136, 0.3394981675496673, -0.37854630883233975, 0.43221561587913865, -0.047183815928172015, 0.40430109093285005, 0.6831440602226162, 0.27649078947951705, -1.6664213645385508, -0.3328138884351746, -0.6686276609175331, -0.9093180606867393]\n",
      "iter:17\n",
      "w: [0.7090382322303439, 0.14875974316242174, 0.3131225496097004, -0.9642562360118443, 0.29931487416739566, 1.2469320534764214, -0.2136893199603249, -0.42571112990484933, 0.34776800227139515, -0.39620311776233963, 0.4467627857364783, -0.05618489532677288, 0.41375530711155634, 0.7112115242872562, 0.30288894318648024, -1.7204761577827474, -0.3428432562746063, -0.6939666992818952, -0.9443414163459253]\n",
      "iter:18\n",
      "w: [0.7329044755919177, 0.15093408736171834, 0.3210277580307024, -0.9894891689757307, 0.30874326974092275, 1.2843255450191382, -0.2171300078491035, -0.43736072740088694, 0.35577267425006043, -0.41304394260476845, 0.4607216021549229, -0.06491370074276534, 0.422947075247345, 0.7378716028031354, 0.328498833440739, -1.7731182942183688, -0.3525719694978748, -0.7183483589746492, -0.9784695091163789]\n",
      "iter:19\n",
      "w: [0.7561133995570936, 0.15286045515640212, 0.328760690901024, -1.0139537508210092, 0.31788682371577265, 1.3203359878921699, -0.22024989032144238, -0.44872754933949704, 0.3635356504637764, -0.4291288733368194, 0.47414174564472794, -0.07339563949692657, 0.4318965531986031, 0.7632395717459113, 0.35339902389681255, -1.8244507576736042, -0.36203068772373537, -0.7418485369835647, -1.0117573172957148]\n",
      "iter:20\n",
      "w: [0.7787079892539899, 0.15456200602459644, 0.33633658450314596, -1.0377123132497756, 0.3267748670740448, 1.3550649489120608, -0.2230780070832732, -0.4598350016169348, 0.3710770468508463, -0.44451297113313276, 0.487067601013812, -0.08165321702581137, 0.44062129776518627, 0.7874193002477285, 0.37765818433851467, -1.8745642981534274, -0.3712449958974367, -0.7645357216530283, -1.0442537275202144]\n",
      "iter:21\n",
      "w: [0.8007262529140036, 0.1560594772059649, 0.34376827002154436, -1.060818996362751, 0.3354319455237139, 1.3886035518622473, -0.22564033126798433, -0.4707031942919707, 0.3784142461967869, -0.4592466165100184, 0.4995387984981119, -0.08970626642269312, 0.44913675622087285, 0.8105044087079029, 0.4013360928412452, -1.9235394849020984, -0.3802364452138948, -0.7864716135654638, -1.0760025700060472]\n",
      "iter:22\n",
      "w: [0.8222020921833231, 0.15737146972957614, 0.3510666965898703, -1.0833211570708576, 0.34387877721624305, 1.4210338238029174, -0.2279601474838501, -0.4813495913406772, 0.38556238422571915, -0.4733758770600258, 0.5115907340536995, -0.09757221648482109, 0.45745663199363035, 0.83257935031115, 0.424484683802042, -1.971448290683485, -0.38902335410334277, -0.8077117662399449, -1.1070434246350234]\n",
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      "iter:24\n",
      "w: [0.8636454670864389, 0.15950416732792658, 0.3653003329720429, -1.1266739678034468, 0.360209732509703, 1.482858682861421, -0.2319538253007387, -0.5020364049989126, 0.399343017076967, -0.49998612479593435, 0.5345600846495382, -0.11280213572953302, 0.47355734286275886, 0.8739965366602681, 0.46936837668843867, -2.064318924528685, -0.406044247183912, -0.8483000328258562, -1.1671419296079542]\n",
      "iter:25\n",
      "w: [0.8836656471038739, 0.1603534255734902, 0.3722509777005583, -1.1475945098423088, 0.36812206865863517, 1.5123813016864462, -0.23366347464932266, -0.5121023178222437, 0.4059976428045398, -0.5125408857080916, 0.5455312417781026, -0.12019132149050894, 0.48135908820857093, 0.8934702516155534, 0.491176732355382, -2.109391808862334, -0.41430363948916343, -0.8677339255435279, -1.1962626100073512]\n",
      "iter:26\n",
      "w: [0.9032494513148862, 0.16107466037129672, 0.3790996098764867, -1.1680516458111565, 0.375881399398912, 1.5410531989440968, -0.23520263801690178, -0.521997936755754, 0.412507915726925, -0.5246394405006506, 0.5561913605853828, -0.12744429189123818, 0.48900738662403054, 0.9121982395725802, 0.5126038144468337, -2.1536219340679157, -0.42240998873736496, -0.8866446594233551, -1.2248021125938482]\n",
      "iter:27\n",
      "w: [0.922417947304039, 0.1616788775625432, 0.38585187847365326, -1.1880719724770439, 0.38349771870651894, 1.5689250594879982, -0.2365851687319244, -0.5317328604974513, 0.41888219447126124, -0.5363113853272858, 0.5665610101206564, -0.13457018378364388, 0.49651041016127917, 0.9302320302856513, 0.5336755563163902, -2.197052985176947, -0.43037247070539114, -0.9050655253342557, -1.2527861760416592]\n",
      "iter:28\n",
      "w: [0.9411905625141772, 0.16217602342568374, 0.39251281995973497, -1.2076795636593056, 0.3909798492859816, 1.5960432798599258, -0.2378236155362006, -0.5413157299328164, 0.4251280259261702, -0.5475838798535487, 0.5766587595378964, -0.14157706484455113, 0.5038756138194018, 0.9476185390802628, 0.5544146643308008, -2.2397248835085883, -0.43819924629378326, -0.9230267199596871, -1.2802386973829956]\n",
      "iter:29\n",
      "w: [0.9595852741409165, 0.1625750990706656, 0.3990869434363314, -1.2268963046481758, 0.39833562760535696, 1.6224504300557419, -0.23892936390516475, -0.550754351175396, 0.43125225536528544, -0.5584818760317878, 0.5865014124117355, -0.14847207604172713, 0.5111098184106876, 0.9644005543745499, 0.5748410753847142, -2.281674207406961, -0.4458976170440247, -0.9405556885568458, -1.3071819291635138]\n",
      "iter:30\n",
      "w: [0.9776187688173722, 0.16288426192335587, 0.40557830114418625, -1.2457421711424088, 0.4055720540203952, 1.6481856556449563, -0.2399127606410839, -0.5600557988963532, 0.43726111794043027, -0.5690283247125373, 0.5961042113291977, -0.1552615548230238, 0.5182192814229061, 0.9806171682798118, 0.5949723477012533, -2.322934555715983, -0.45347415171844135, -0.9576774276294637, -1.3336366472304257]\n",
      "iter:31\n",
      "w: [0.9953065780883319, 0.16311091570219172, 0.4119905475305536, -1.2642354633336523, 0.41269541537110693, 1.6732850291165284, -0.24078322381995113, -0.5692265039754737, 0.4431603151835325, -0.5792443618829073, 0.6054810164393999, -0.161951141381158, 0.5252097580923409, 0.9963041571084452, 0.6148239942141389, -2.3635368636365333, -0.4609347900399002, -0.9744147517426334, -1.3596222946768448]\n",
      "iter:32\n",
      "w: [1.0126631942929332, 0.1632617901510506, 0.41832698921506856, -1.2823930035348632, 0.4197113857459025, 1.6977818578508115, -0.2415493398948393, -0.578272328478973, 0.44895507937375845, -0.5891494763448589, 0.614644461299508, -0.1685458702019946, 0.5320865543832194, 1.011494317894958, 0.634409766848547, -2.403509678558329, -0.4682849282896805, -0.9907885285272439, -1.3851571062550208]\n",
      "iter:33\n",
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      "iter:67\n",
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      "iter:68\n",
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      "iter:70\n",
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      "iter:71\n",
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      "iter:72\n",
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      "iter:73\n",
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      "iter:77\n",
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      "iter:78\n",
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      "iter:83\n",
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      "iter:85\n",
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      "iter:86\n",
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      "iter:87\n",
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      "iter:88\n",
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      "iter:89\n",
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      "iter:91\n",
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      "iter:92\n",
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      "iter:93\n",
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      "iter:94\n",
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      "iter:96\n",
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      "iter:97\n",
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      "iter:98\n",
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      "iter:99\n",
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      "iter:100\n",
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      "iter:101\n",
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      "iter:102\n",
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      "iter:103\n",
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      "iter:104\n",
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      "iter:105\n",
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      "iter:106\n",
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      "iter:107\n",
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      "iter:108\n",
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      "iter:109\n",
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      "iter:110\n",
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      "iter:111\n",
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      "iter:112\n",
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      "iter:113\n",
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      "iter:114\n",
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      "iter:115\n",
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      "iter:116\n",
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      "iter:117\n",
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      "iter:118\n",
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      "iter:119\n",
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      "iter:120\n",
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      "iter:121\n",
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      "iter:122\n",
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      "iter:123\n",
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      "iter:124\n",
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      "iter:125\n",
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      "iter:126\n",
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      "iter:127\n",
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      "iter:128\n",
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      "iter:129\n",
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      "iter:130\n",
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      "iter:131\n",
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      "iter:132\n",
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      "iter:133\n",
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      "iter:134\n",
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      "iter:135\n",
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      "iter:136\n",
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      "iter:137\n",
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      "iter:138\n",
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      "iter:139\n",
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      "iter:140\n",
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      "iter:141\n",
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      "iter:142\n",
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      "iter:143\n",
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      "iter:144\n",
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      "iter:145\n",
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      "iter:179\n"
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    {
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      "iter:182\n",
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      "iter:183\n",
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      "iter:184\n",
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      "iter:185\n",
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      "iter:186\n",
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      "iter:187\n",
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      "iter:188\n",
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      "iter:189\n",
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      "iter:190\n",
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      "iter:191\n",
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      "iter:192\n",
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      "iter:193\n",
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      "iter:194\n",
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      "iter:195\n",
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      "iter:196\n",
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      "iter:197\n",
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      "iter:198\n",
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      "iter:199\n",
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      "iter:200\n",
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      "iter:201\n",
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      "iter:202\n",
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      "iter:203\n",
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      "iter:204\n",
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      "iter:205\n",
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      "iter:206\n",
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      "iter:207\n",
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      "iter:208\n",
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      "iter:209\n",
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      "iter:210\n",
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      "iter:211\n",
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      "iter:212\n",
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      "iter:213\n",
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      "iter:214\n",
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      "iter:215\n",
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      "iter:216\n",
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      "iter:217\n",
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      "iter:218\n",
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      "iter:219\n",
      "w: [2.501222567189322, 0.07660294489544033, 1.0698479288060312, -2.9388812234297097, 1.1222929054819277, 3.6173152897110246, -0.1743646962486524, -1.4772328152602547, 0.984904352705724, -1.2755231410610546, 1.3456065768270018, -0.7916103080415675, 1.1708068359801684, 2.0455876865092146, 2.500103832194783, -6.190962116652394, -1.1966302261985695, -2.3444255784053842, -3.641866792210208]\n",
      "iter:220\n",
      "w: [2.5058658398161295, 0.07634355634284089, 1.071956224472846, -2.9442804763682817, 1.1246589207134552, 3.6232387653553975, -0.17411802990946795, -1.4801154164075445, 0.9866644219875916, -1.2776219907893842, 1.347765239679269, -0.7934581975537061, 1.1728304543768013, 2.048733564294805, 2.505621601353706, -6.203080369136732, -1.1990524723305254, -2.348548991370978, -3.648978609221488]\n",
      "iter:221\n",
      "w: [2.5104939909600983, 0.07608595862721743, 1.0740570452750382, -2.9496626182056467, 1.1270174235551296, 3.6291436942922317, -0.17387300656885205, -1.482987745787902, 0.9884189706414895, -1.2797147925315548, 1.3499161919713443, -0.7952985492252712, 1.1748471084487768, 2.051870365493183, 2.511116750142935, -6.215157217606067, -1.2014668720631867, -2.3526582673169285, -3.6560672229385505]\n",
      "iter:222\n",
      "w: [2.5151071344059925, 0.07583013639646849, 1.0761504462805862, -2.955027769819105, 1.1293684656749716, 3.6350302145238507, -0.17362961307926456, -1.4858498790247703, 0.9901680375147062, -1.281801589785486, 1.3520594948236297, -0.7971314237389315, 1.176856849871407, 2.0549981555844776, 2.51658946203356, -6.2271929660804215, -1.2038734802403164, -2.35675351499188, -3.663132805900806]\n",
      "iter:223\n",
      "w: [2.5197053825431004, 0.07557607444042416, 1.078236481962845, -2.960376050712862, 1.1317120981921829, 3.640898462313682, -0.17338783639444272, -1.488701890921616, 0.9919116610149595, -1.2838824254751595, 1.3541952086005045, -0.7989568810859182, 1.1788597297318153, 2.058116999181878, 2.5220399183915836, -6.23918791516209, -1.2062723511147804, -2.360834841826124, -3.670175528566296]\n",
      "iter:224\n",
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      "iter:225\n",
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      "iter:226\n",
      "w: [2.533411858550867, 0.07482430022714286, 1.0844509330542977, -2.9763208439694617, 1.1386990412494076, 3.6583949082237335, -0.17267207822321484, -1.4971979345452533, 0.9971102489040188, -1.2900895840198685, 1.360557408043383, -0.8043893398730136, 1.1848277021735987, 2.06742048448767, 2.538259536982307, -6.274930921870802, -1.2134230737638876, -2.372996352261941, -3.6911682088584414]\n",
      "iter:227\n",
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      "iter:228\n",
      "w: [2.542477032448858, 0.07433164623559846, 1.0885580464844287, -2.9868684835865715, 1.1433208684577998, 3.669970265947685, -0.17220275549920047, -1.5028126924498937, 1.000549442271178, -1.2941986439951496, 1.3647620027423903, -0.8079749628390015, 1.188772953582673, 2.0735792226143634, 2.5489645713972164, -6.2985609578574895, -1.218152504487458, -2.381036333842295, -3.7050520620470224]\n",
      "iter:229\n",
      "w: [2.546988193651844, 0.0740878343374325, 1.0906010018789365, -2.992117975509635, 1.1456210870873607, 3.6757316470270704, -0.17197041132868246, -1.5056055026743094, 1.0022611883235062, -1.2962445809231498, 1.3668534089279691, -0.809757139500363, 1.1907357050599976, 2.0766456976380994, 2.554285189090781, -6.3103172381380555, -1.22050605881256, -2.3850363205027216, -3.711961090234362]\n",
      "iter:230\n",
      "w: [2.5514852091047495, 0.07384568013307773, 1.0926369572824561, -2.9973513965469403, 1.1479142392154684, 3.681475663316345, -0.17173959546389322, -1.5083886931582815, 1.0039677481059888, -1.2982848415808494, 1.3689376284407526, -0.8115323003794648, 1.1926919368417674, 2.07970365554373, 2.5595847643375826, -6.322034731707387, -1.2228522397516528, -2.3890231031775477, -3.718848395851176]\n",
      "iter:231\n",
      "w: [2.555968180836472, 0.07360516951158243, 1.0946659626939812, -3.002568855956365, 1.1502003718385014, 3.687202438218516, -0.1715102956631093, -1.5111623325405819, 1.0056691567447176, -1.3003194646772933, 1.3710147160270447, -0.8133005002767913, 1.1946416956160493, 2.0827531545793168, 2.564863462705518, -6.333713713582892, -1.225191097122602, -2.392996779490755, -3.725714133883789]\n",
      "iter:232\n",
      "w: [2.560437209674536, 0.0733662884947223, 1.0966880675866857, -3.007770461801422, 1.152479531469065, 3.6929120936510103, -0.1712824997840021, -1.513926488736117, 1.0073654489830939, -1.3023484884380547, 1.3730847257811016, -0.8150617933842778, 1.1965850275570278, 2.085794252263001, 2.570121447910997, -6.345354455790458, -1.2275226802233337, -2.3969574459270335, -3.7325584575222104]\n",
      "iter:233\n",
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      "iter:234\n",
      "w: [2.5693338360890174, 0.07289336001926909, 1.100711771121411, -3.018126539188198, 1.1570171154239646, 3.7042805264992453, -0.17083137171636179, -1.5194266196659574, 1.0107428213532024, -1.3063898884905993, 1.3772037249716107, -0.8185638730053956, 1.2004525931113759, 2.091851470078061, 2.580575924597805, -6.368522294606068, -1.2321642182493135, -2.4048401295185107, -3.746183465565765]\n",
      "iter:235\n",
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      "iter:236\n",
      "w: [2.578175871668981, 0.07242678549499615, 1.1047084534206857, -3.0284204700028465, 1.1615273537544206, 3.7155819084318806, -0.17038611609643112, -1.5248896151589633, 1.0141001357246873, -1.310409338206287, 1.3812950461162095, -0.8220389609256754, 1.2042949929029563, 2.0978757550392286, 2.590949468073438, -6.391540366152812, -1.2367772380852962, -2.4126719037173796, -3.759724610646956]\n",
      "iter:237\n",
      "w: [2.5825766577409284, 0.07219584739880969, 1.1066967799003824, -3.0335443884156748, 1.1637723296370222, 3.721207745014044, -0.17016566114395204, -1.5276073494875655, 1.0157713541131095, -1.3124109223615024, 1.383330456019227, -0.8237665122488765, 1.206206865823043, 2.1008756841129475, 2.5961062802006327, -6.402993888686057, -1.2390731716041175, -2.416568929401799, -3.7664640992615803]\n",
      "iter:238\n",
      "w: [2.5869640817158506, 0.07196645776541853, 1.1086784920450714, -3.0386530775469223, 1.1660106018066874, 3.7268171638063343, -0.16994663932542695, -1.5303159934566009, 1.0174376568383983, -1.314407126865112, 1.3853590995318612, -0.8254874696190044, 1.2081125785750602, 2.1038675423473086, 2.6012433240040824, -6.414410743250101, -1.2413621161170525, -2.420453501173789, -3.7731830564599953]\n",
      "iter:239\n",
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      "iter:240\n",
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      "iter:241\n",
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      "iter:242\n",
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      "iter:243\n",
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      "iter:244\n",
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      "iter:245\n",
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      "iter:246\n",
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      "iter:247\n",
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      "iter:248\n",
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      "iter:249\n",
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      "iter:250\n",
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      "iter:251\n",
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      "iter:252\n",
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      "iter:253\n",
      "w: [2.6512327729100567, 0.06870282380516603, 1.1376406357065825, -3.113521598495061, 1.1988086887337444, 3.809061638087393, -0.166825722367859, -1.5698962330320514, 1.0418634478439623, -1.3437275389343644, 1.4150093428282235, -0.8505434142581837, 1.235987090467195, 2.147811362765739, 2.6760259693853334, -6.581428814262639, -1.2748877132312768, -2.477285823169071, -3.871596163757366]\n",
      "iter:254\n",
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      "iter:255\n",
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      "iter:256\n",
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      "iter:257\n",
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      "iter:258\n",
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      "iter:259\n",
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      "iter:260\n",
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      "iter:261\n",
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      "iter:262\n",
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      "iter:263\n",
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      "iter:264\n",
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      "iter:265\n",
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      "iter:266\n",
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      "iter:267\n",
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      "iter:268\n",
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      "iter:269\n",
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      "iter:270\n",
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      "iter:271\n",
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      "iter:272\n",
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      "iter:273\n",
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      "iter:274\n",
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      "iter:275\n",
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      "iter:276\n",
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      "iter:277\n",
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      "iter:278\n",
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      "iter:279\n",
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      "iter:280\n",
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      "iter:281\n",
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      "iter:282\n",
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      "iter:283\n",
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      "iter:284\n",
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      "iter:285\n",
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      "iter:286\n",
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      "iter:287\n",
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      "iter:288\n",
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      "iter:289\n",
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      "iter:290\n",
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      "iter:291\n",
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      "iter:292\n",
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      "iter:293\n",
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      "iter:294\n",
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      "iter:295\n",
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      "iter:296\n",
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      "iter:298\n",
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      "iter:299\n",
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      "iter:300\n",
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      "iter:302\n",
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      "iter:303\n",
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      "iter:304\n",
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      "iter:305\n",
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      "iter:306\n",
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      "iter:307\n",
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      "iter:308\n",
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      "iter:309\n",
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      "iter:310\n",
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      "iter:311\n",
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      "iter:312\n",
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      "iter:313\n",
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      "iter:314\n",
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      "iter:315\n",
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      "iter:316\n",
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      "iter:317\n",
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      "iter:318\n",
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      "iter:319\n",
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      "iter:320\n",
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      "iter:321\n",
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      "iter:322\n",
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      "iter:323\n",
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      "iter:324\n",
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      "iter:325\n",
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      "iter:326\n",
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      "iter:327\n",
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      "iter:328\n",
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      "iter:329\n",
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      "iter:330\n",
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      "iter:331\n",
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      "iter:332\n",
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      "iter:333\n",
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      "iter:334\n",
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      "iter:335\n",
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      "iter:336\n",
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      "iter:337\n",
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      "iter:338\n",
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      "iter:339\n",
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      "iter:340\n",
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      "iter:341\n",
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      "iter:342\n",
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      "iter:343\n",
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      "iter:344\n",
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      "iter:345\n",
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      "iter:346\n",
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      "iter:347\n",
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      "iter:348\n",
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      "iter:349\n",
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      "iter:350\n",
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      "iter:351\n",
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      "iter:352\n",
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      "iter:353\n",
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      "iter:354\n",
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      "iter:355\n",
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      "iter:356\n",
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      "iter:357\n",
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      "iter:358\n",
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      "iter:359\n",
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      "iter:360\n",
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      "iter:361\n",
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      "iter:362\n",
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      "iter:363\n",
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      "iter:364\n",
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      "iter:365\n",
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      "iter:366\n",
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      "iter:367\n",
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      "iter:368\n",
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      "iter:369\n"
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    {
     "name": "stdout",
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      "iter:370\n",
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      "iter:383\n",
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      "iter:392\n",
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      "iter:393\n",
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      "iter:394\n",
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      "iter:395\n",
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      "iter:396\n",
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      "iter:398\n",
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      "iter:400\n",
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      "iter:401\n",
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      "iter:402\n",
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      "iter:403\n",
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      "iter:404\n",
      "w: [3.179727490117536, 0.04818833696699468, 1.37109383420775, -3.730279320746464, 1.468571961975307, 4.490220180298821, -0.147017643827428, -1.8884479619083694, 1.2435031685289057, -1.589866495109559, 1.6547473169743392, -1.0466819757237635, 1.4622668101333893, 2.516683252958362, 3.2610668700044916, -7.938542493618603, -1.5496908812591608, -2.9402095018772365, -4.679832331614621]\n",
      "iter:405\n",
      "w: [3.1826885657666626, 0.04810157234948024, 1.372379845923439, -3.7337356330113525, 1.4700815091578516, 4.494057650821042, -0.1469332007201146, -1.8901998830215827, 1.2446352937564926, -1.591267239055222, 1.6560731531450084, -1.0477372684443174, 1.4635206650596024, 2.518782430073589, 3.2642138960926412, -7.946066963216913, -1.5512244372854724, -2.94278438049686, -4.684354122743589]\n",
      "iter:406\n",
      "w: [3.1856440788440303, 0.04801524331679598, 1.3736632235845845, -3.737185428038174, 1.471588188326721, 4.497888110599902, -0.14684917605844208, -1.8919481804927876, 1.245765307945845, -1.592665554180804, 1.6573963359877317, -1.0487901600728555, 1.464772023448508, 2.5208779678529654, 3.267353763133256, -7.953576484913512, -1.5527550379538937, -2.9453542490670053, -4.688867336494925]\n",
      "iter:407\n",
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      "iter:408\n",
      "w: [3.1915385060527486, 0.04784388053872685, 1.3762221222317097, -3.74406556914204, 1.4745929883114555, 4.505528106188076, -0.14668237123667727, -1.8954339671295155, 1.2480190363231283, -1.5954549329431935, 1.6600347869939223, -1.0508887855032458, 1.4672672925022618, 2.525058177838641, 3.273612156052176, -7.968550934379623, -1.5558074208658819, -2.9504790395138736, -4.697868168922051]\n",
      "iter:409\n",
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      "iter:410\n",
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      "iter:411\n",
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      "iter:412\n",
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      "iter:413\n",
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      "iter:414\n",
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      "iter:415\n",
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      "iter:416\n",
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      "iter:417\n",
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      "iter:418\n",
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      "iter:419\n",
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      "iter:420\n",
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      "iter:421\n",
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      "iter:422\n",
      "w: [3.2321934899093883, 0.04669094351392567, 1.3938481033230465, -3.7915163206282556, 1.4953141260859302, 4.558243618457457, -0.14555953930432866, -1.9194406096430252, 1.2635650448999516, -1.6147152670642277, 1.6782154379377503, -1.0653189241691887, 1.4844625823162247, 2.5539221034244637, 3.316645068577563, -8.071745736628696, -1.5768522303424308, -2.9858074194610835, -4.75993958250218]\n",
      "iter:423\n",
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      "iter:424\n",
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      "iter:425\n",
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      "iter:426\n",
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      "iter:427\n",
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      "iter:428\n",
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      "iter:429\n",
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      "iter:430\n",
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      "iter:431\n",
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      "iter:432\n",
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      "iter:433\n",
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      "iter:434\n",
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      "iter:435\n",
      "w: [3.26902986688938, 0.045688963510621836, 1.4097842868050856, -3.8345053158511972, 1.5140835664633445, 4.606038518357322, -0.14458292758246624, -1.9411398832179334, 1.27765313208347, -1.6321979607371189, 1.6946631400970176, -1.0783282795410942, 1.500020505968535, 2.5801221318629595, 3.35544150669636, -8.165119166471474, -1.59590823893804, -3.0177908526693615, -4.816167053646188]\n",
      "iter:436\n",
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      "iter:437\n",
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      "iter:438\n",
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      "iter:439\n",
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      "iter:440\n",
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      "iter:441\n",
      "w: [3.285746420342199, 0.0452472687794058, 1.4170057623776051, -3.8540122841063185, 1.5225995209193566, 4.627737461240814, -0.14415218025372636, -1.9509710435581085, 1.284047041778889, -1.6401412323969553, 1.7021195191477476, -1.0842120801385302, 1.507073956889548, 2.5920261686439177, 3.3729883709611137, -8.20745308296706, -1.6045521765858177, -3.0322970736892927, -4.841679043239483]\n",
      "iter:442\n",
      "w: [3.288515453577952, 0.04517487455466696, 1.4182013524867698, -3.8572434324820493, 1.5240100518517483, 4.631332360782928, -0.14408156654699464, -1.952598581392366, 1.285106206249424, -1.641457567580104, 1.7033541859209638, -1.0851855299763307, 1.5082419287600972, 2.59399887247124, 3.3758914405713023, -8.214463187173795, -1.6059837844792801, -3.034699500637531, -4.84590474345168]\n",
      "iter:443\n",
      "w: [3.2912796606360084, 0.04510282353271668, 1.4193946842670366, -3.8604689185241248, 1.525418094708394, 4.634921150134502, -0.14401128374729744, -1.9542230130003801, 1.2861635351921947, -1.6427717666844084, 1.7045865730937826, -1.0861569512514595, 1.5094077507130115, 2.5959683758286225, 3.3787884650832476, -8.221460411519644, -1.6074128328575235, -3.03709760750942, -4.850123003846008]\n",
      "iter:444\n",
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      "iter:445\n",
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      "iter:446\n",
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      "iter:447\n",
      "w: [3.302288579478753, 0.04481800885766996, 1.4241456068955256, -3.8733146496921536, 1.5310255676313824, 4.649215637991892, -0.1437334211091197, -1.9606899234909103, 1.2903746279485304, -1.648007343902443, 1.7094935034346743, -1.090022526397444, 1.5140497046767636, 2.6038145967948676, 3.3903166371153204, -8.249321497302489, -1.6131036208802818, -3.0466471630622216, -4.866922191892403]\n",
      "iter:448\n",
      "w: [3.305028919040736, 0.044747642030828476, 1.4253277806504627, -3.8765121307953017, 1.5324213063425902, 4.652774199585818, -0.14366476259530192, -1.9622990080515843, 1.2914228781204893, -1.6493109684750684, 1.7107146253682672, -1.0909839361106826, 1.515204900604162, 2.6057682564853364, 3.393183828352406, -8.256255060022927, -1.6145200134487379, -3.049023915307348, -4.871103660300079]\n",
      "iter:449\n",
      "w: [3.3077645370681275, 0.04467760579243291, 1.4265077491441625, -3.879704071443421, 1.5338146111079838, 4.656326779414902, -0.14359642299446043, -1.9639050594975558, 1.2924693320502232, -1.6506124990519802, 1.7119335204272015, -1.0919433693624652, 1.516357995694316, 2.6077187787859963, 3.3960451301791807, -8.263176035905717, -1.6159339028267945, -3.051396445089471, -4.875277850631644]\n",
      "iter:450\n",
      "w: [3.3104954506483972, 0.04460789809601073, 1.4276855210333044, -3.8828904915473332, 1.5352054907694261, 4.659873398461834, -0.14352840035979827, -1.9655080897559118, 1.2935139961558648, -1.6519119425174396, 1.713150197211546, -1.0929008346389242, 1.5175089979568261, 2.60966617401574, 3.398900567951212, -8.270084472774945, -1.6173452982130812, -3.0537647683369613, -4.879444789300331]\n",
      "iter:451\n",
      "w: [3.313221676770332, 0.04453851691068423, 1.4288611049220419, -3.8860714109053296, 1.5365939541184819, 4.663414077591423, -0.14346069275908857, -1.9671081106815749, 1.2945568768193347, -1.6532093057194417, 1.7143646642689816, -1.0938563403710775, 1.518657915353643, 2.6116104524390407, 3.401750166858682, -8.276980418171469, -1.6187542087534068, -3.0561289008830417, -4.883604502567369]\n",
      "iter:452\n",
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      "iter:453\n",
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      "iter:454\n",
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      "iter:455\n",
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      "iter:456\n",
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      "iter:457\n",
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      "iter:458\n",
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      "iter:459\n",
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      "iter:460\n",
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      "iter:461\n",
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      "iter:462\n",
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      "iter:463\n",
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      "iter:464\n",
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      "iter:465\n",
      "w: [3.3509059449137877, 0.04360036263231582, 1.4450942362214827, -3.9300375302210577, 1.5557835350658993, 4.712371305709385, -0.14254481647414818, -1.9891988956231255, 1.308973434751961, -1.671157713780048, 1.7311398474409174, -1.1070322626101965, 1.5345281965367088, 2.6385087077836733, 3.4410451955605232, -8.372238017041811, -1.6382230469178716, -3.0887953796033423, -4.94109617590348]\n",
      "iter:466\n",
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      "iter:467\n",
      "w: [3.3562172928368574, 0.043471224588353126, 1.4473797029524245, -3.936233751780216, 1.5584877341224013, 4.719273697910223, -0.1424186936122415, -1.992308579008747, 1.3110054908837818, -1.6736896527229292, 1.7335023928078352, -1.1088846072587506, 1.5367633700720467, 2.6423031927420797, 3.4465695993974306, -8.385654434323433, -1.6409661028826885, -3.093397649194421, -4.949198118700995]\n",
      "iter:468\n",
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      "iter:469\n",
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      "iter:470\n",
      "w: [3.364151255339932, 0.04327971993819947, 1.4507925519956013, -3.945489274389911, 1.5625269960823145, 4.7295853153768075, -0.1422316373473262, -1.9969519933471749, 1.3140409877524486, -1.6774728081282557, 1.737030689755391, -1.111649461313024, 1.5401014748646364, 2.647972816587685, 3.4548155012881834, -8.405691233028676, -1.6450631794100061, -3.100271573757485, -4.961300083783655]\n",
      "iter:471\n",
      "w: [3.3667871547856874, 0.04321646531393679, 1.4519261055057366, -3.9485641707035506, 1.5638689053048223, 4.7330114042525215, -0.14216984600761234, -1.998494211013315, 1.3150494864315883, -1.6787299506608213, 1.7382026803450599, -1.1125674658055416, 1.5412102968704433, 2.6498568341805178, 3.4575533702361136, -8.412346915859347, -1.6464242358533503, -3.1025550774036117, -4.965320580214271]\n",
      "iter:472\n",
      "w: [3.3694187020888355, 0.04315349791906899, 1.4530576402901823, -3.9516339575292014, 1.5652085718816122, 4.736431965726081, -0.14210833227560246, -2.0000336526173044, 1.3160563278027737, -1.6799851488288013, 1.7393726293453295, -1.113483675865853, 1.5423171908554065, 2.6517379386542834, 3.460285893497394, -8.418991043999755, -1.6477829880122252, -3.104834702186599, -4.9693343696762655]\n",
      "iter:473\n",
      "w: [3.3720459122557234, 0.04309081603279944, 1.4541871638985373, -3.954698652398008, 1.5665460035905692, 4.7398470182907975, -0.14204709450945605, -2.0015703285647546, 1.31706151751836, -1.6812384087479355, 1.7405405442546176, -1.1143980988233706, 1.543422163824363, 2.6536161391748365, 3.463013092958049, -8.425623659299081, -1.6491394439686333, -3.1071104620311933, -4.9733414753752845]\n",
      "iter:474\n",
      "w: [3.3746688002104817, 0.04302841794704274, 1.4553146838367073, -3.9577582727468195, 1.5678812081674067, 4.743256580341478, -0.14198613107926494, -2.003104249201207, 1.3180650612003584, -1.6824897365034277, 1.7417064325279654, -1.1153107419620771, 1.5445252227424684, 2.655491444862225, 3.4657349903679027, -8.432244803370423, -1.6504936117603515, -3.1093823707831274, -4.977341920390169]\n",
      "iter:475\n",
      "w: [3.377287380795658, 0.04296630196631402, 1.4564402075672445, -3.9608128359188917, 1.5692141933059816, 4.746660670175166, -0.1419254403669513, -2.0046354248125993, 1.3190669644406625, -1.6837391381501663, 1.742870301577384, -1.1162216125208975, 1.5456263745355043, 2.657363864791019, 3.4684516073416995, -8.438854517592615, -1.651845499381263, -3.111650442209739, -4.98133572767393]\n",
      "iter:476\n",
      "w: [3.379901668772841, 0.042904466407619475, 1.4575637425096855, -3.9638623591645845, 1.570544966658605, 4.750059305991885, -0.1418650207661666, -2.006163865625724, 1.320067232801273, -1.6849866197129424, 1.7440321587721965, -1.117130717694066, 1.5467256260901816, 2.6592334079906412, 3.47116296536021, -8.445452843112026, -1.6531951147816861, -3.1139146900005854, -4.985322920054698]\n",
      "iter:477\n",
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      "iter:478\n",
      "w: [3.3851174255485024, 0.042781629886161146, 1.459804875495344, -3.9699463544179268, 1.5731999084093629, 4.75684028789375, -0.14174498853184028, -2.0092125834713688, 1.3220628869832796, -1.6874758465365802, 1.746349866863878, -1.1189436604391148, 1.5489184558377542, 2.662963900096258, 3.4765699897911624, -8.458615491476301, -1.6558875605064667, -3.1184317690479375, -4.993277550801108]\n",
      "iter:479\n",
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      "iter:480\n",
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      "iter:481\n",
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      "iter:482\n",
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      "iter:483\n",
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      "iter:484\n",
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      "iter:485\n",
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      "iter:486\n",
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      "iter:487\n",
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      "iter:488\n",
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      "iter:489\n",
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      "iter:490\n",
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      "iter:491\n",
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      "iter:492\n",
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      "iter:493\n",
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      "iter:494\n",
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      "iter:495\n",
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      "iter:496\n",
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      "iter:497\n",
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      "iter:498\n",
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      "iter:499\n",
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      "iter:500\n",
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      "iter:501\n",
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      "iter:502\n",
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      "iter:503\n",
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      "iter:504\n",
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      "iter:505\n",
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      "iter:506\n",
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      "iter:507\n",
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      "iter:508\n",
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      "iter:509\n",
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      "iter:510\n",
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      "iter:511\n",
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      "iter:512\n",
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      "iter:513\n",
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      "iter:514\n",
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      "iter:515\n",
      "w: [3.4786595237199034, 0.040694967858803575, 1.4999049308353434, -4.079036740444595, 1.6207971377840804, 4.878535782712114, -0.13970422199872504, -2.063742727256884, 1.3578586392374161, -1.7322017865810682, 1.7878494278192265, -1.1512808366843295, 1.5881835627350442, 2.72999323843419, 3.573018924946729, -8.694318566011788, -1.7041379532745728, -3.1993756921862238, -5.135894029627019]\n",
      "iter:516\n",
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      "iter:517\n",
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      "iter:518\n",
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      "iter:519\n",
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      "iter:520\n",
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      "iter:521\n",
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      "iter:522\n",
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      "iter:523\n",
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      "iter:524\n",
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      "iter:525\n",
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      "iter:526\n",
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      "iter:527\n",
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      "iter:528\n",
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      "iter:529\n",
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      "iter:530\n",
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      "iter:531\n",
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      "iter:532\n",
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      "iter:533\n",
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      "iter:534\n",
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      "iter:535\n",
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      "iter:536\n",
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      "iter:537\n",
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      "iter:538\n",
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      "iter:539\n",
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      "iter:540\n",
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      "iter:541\n",
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      "iter:542\n",
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      "iter:543\n",
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      "iter:544\n",
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      "iter:545\n",
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      "iter:546\n",
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      "iter:547\n",
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      "iter:548\n",
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      "iter:549\n",
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      "iter:550\n",
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      "iter:551\n",
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      "iter:552\n",
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      "iter:565\n",
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      "iter:566\n",
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      "iter:567\n"
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    {
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      "iter:589\n",
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      "iter:590\n",
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      "iter:591\n",
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      "iter:592\n",
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      "iter:593\n",
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      "iter:594\n",
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      "iter:595\n",
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      "iter:596\n",
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      "iter:597\n",
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      "iter:598\n",
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      "iter:599\n",
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      "iter:600\n",
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      "iter:601\n",
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      "iter:602\n",
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      "iter:603\n",
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      "iter:604\n",
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      "iter:605\n",
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      "iter:606\n",
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      "iter:607\n",
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      "iter:608\n",
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      "iter:609\n",
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      "iter:610\n",
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      "iter:611\n",
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      "iter:612\n",
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      "iter:613\n",
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      "iter:614\n",
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      "iter:615\n",
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      "iter:616\n",
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      "iter:617\n",
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      "iter:618\n",
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      "iter:619\n",
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      "iter:620\n",
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      "iter:621\n",
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      "iter:622\n",
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      "iter:623\n",
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      "iter:624\n",
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      "iter:625\n",
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      "iter:626\n",
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      "iter:627\n",
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      "iter:628\n",
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      "iter:629\n",
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      "iter:630\n",
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      "iter:631\n",
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      "iter:632\n",
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      "iter:633\n",
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      "iter:634\n",
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      "iter:635\n",
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      "iter:636\n",
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      "iter:637\n",
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      "iter:638\n",
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      "iter:639\n",
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      "iter:640\n",
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      "iter:641\n",
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      "iter:642\n",
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      "iter:643\n",
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      "iter:644\n",
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      "iter:645\n",
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      "iter:646\n",
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      "iter:647\n",
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      "iter:648\n",
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      "iter:649\n",
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      "iter:650\n",
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      "iter:651\n",
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      "iter:652\n",
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      "iter:653\n",
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      "iter:654\n",
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      "iter:655\n",
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      "iter:656\n",
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      "iter:657\n",
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      "iter:658\n",
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      "iter:659\n",
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      "iter:660\n",
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      "iter:661\n",
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      "iter:662\n",
      "w: [3.8043562704330967, 0.0349266775976822, 1.6383289567432233, -4.458486150037083, 1.7862721355235676, 5.3032913000622735, -0.13404516120941062, -2.2516834616405705, 1.4825436932988902, -1.8889689843367865, 1.9314887322844871, -1.2616066037598919, 1.724086382680403, 2.964945631921901, 3.902167873865744, -9.510241257201976, -1.8716224112991564, -3.480392743408613, -5.631778800302624]\n",
      "iter:663\n",
      "w: [3.806361507565719, 0.0348973837073587, 1.6391762776402004, -4.46082036700038, 1.7872898160522181, 5.305910631880809, -0.13401635325297073, -2.2528324581617647, 1.4833115301839292, -1.8899383652170454, 1.9323695880561387, -1.2622764904730739, 1.7249196963071136, 2.966398532640618, 3.904166955381073, -9.515244625579237, -1.8726512915652174, -3.4821197858946427, -5.634828605832783]\n",
      "iter:664\n",
      "w: [3.8083642640626554, 0.03486819339595951, 1.6400224976589866, -4.463151671894514, 1.7883062251202617, 5.308526768308639, -0.13398764643967714, -2.2539799445450406, 1.4840784189709668, -1.890906591367886, 1.933249316738729, -1.2629454476069037, 1.7257519419059324, 2.967849703391228, 3.9061632698216244, -9.520241584621713, -1.8736788731126397, -3.483844660866203, -5.637874599559359]\n"
     ]
    }
   ],
   "source": [
    "maxent.loadData(dataset)\n",
    "maxent.train()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predict: {'yes': 0.9999971802186581, 'no': 2.819781341881656e-06}\n"
     ]
    }
   ],
   "source": [
    "print('predict:', maxent.predict(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第6章Logistic回归与最大熵模型-习题\n",
    "\n",
    "### 习题6.1\n",
    "&emsp;&emsp;确认Logistic分布属于指数分布族。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**解答：**  \n",
    "**第1步：**  \n",
    "首先给出指数分布族的定义：  \n",
    "对于随机变量$x$，在给定参数$\\eta$下，其概率分别满足如下形式：$$p(x|\\eta)=h(x)g(\\eta)\\exp(\\eta^Tu(x))$$我们称之为**指数分布族**。  \n",
    "其中：  \n",
    "$x$：可以是标量或者向量，可以是离散值也可以是连续值  \n",
    "$\\eta$：自然参数  \n",
    "$g(\\eta)$：归一化系数  \n",
    "$h(x),u(x)$：$x$的某个函数  \n",
    "\n",
    "----\n",
    "\n",
    "**第2步：**证明伯努利分布属于指数分布族  \n",
    "伯努利分布：$\\varphi$是$y=1$的概率，即$P(Y=1)=\\varphi$  \n",
    "$\\begin{aligned}\n",
    "P(y|\\varphi) \n",
    "&= \\varphi^y (1-\\varphi)^{(1-y)} \\\\\n",
    "&= (1-\\varphi) \\varphi^y (1-\\varphi)^{(-y)} \\\\\n",
    "&= (1-\\varphi) (\\frac{\\varphi}{1-\\varphi})^y \\\\\n",
    "&= (1-\\varphi) \\exp\\left(y \\ln \\frac{\\varphi}{1-\\varphi} \\right) \\\\\n",
    "&= \\frac{1}{1+e^\\eta} \\exp (\\eta y)\n",
    "\\end{aligned}$  \n",
    "其中，$\\displaystyle \\eta=\\ln \\frac{\\varphi}{1-\\varphi} \\Leftrightarrow \\varphi = \\frac{1}{1+e^{-\\eta}}$  \n",
    "将$y$替换成$x$，可得$\\displaystyle P(x|\\eta) = \\frac{1}{1+e^\\eta} \\exp (\\eta x)$\n",
    "对比可知，伯努利分布属于指数分布族，其中$\\displaystyle h(x) = 1, g(\\eta)= \\frac{1}{1+e^\\eta}, u(x)=x$  \n",
    "\n",
    "----\n",
    "\n",
    "**第3步：**  \n",
    "广义线性模型（GLM）必须满足三个假设：\n",
    "1. $y | x;\\theta \\sim ExponentialFamily(\\eta)$，即假设预测变量$y$在给定$x$，以$\\theta$为参数的条件概率下，属于以$\\eta$作为自然参数的指数分布族；  \n",
    "2. 给定$x$，求解出以$x$为条件的$T(y)$的期望$E[T(y)|x]$，即算法输出为$h(x)=E[T(y)|x]$  \n",
    "3. 满足$\\eta=\\theta^T x$，即自然参数和输入特征向量$x$之间线性相关，关系由$\\theta$决定，仅当$\\eta$是实数时才有意义，若$\\eta$是一个向量，则$\\eta_i=\\theta_i^T x$\n",
    "\n",
    "----\n",
    "\n",
    "**第4步：**推导伯努利分布的GLM  \n",
    "已知伯努利分布属于指数分布族，对给定的$x,\\eta$，求解期望：$$\\begin{aligned}\n",
    "h_{\\theta}(x) \n",
    "&= E[y|x;\\theta] \\\\\n",
    "&= 1 \\cdot p(y=1)+ 0 \\cdot p(y=0) \\\\\n",
    "&= \\varphi \\\\\n",
    "&= \\frac{1}{1+e^{-\\eta}} \\\\\n",
    "&= \\frac{1}{1+e^{-\\theta^T x}}\n",
    "\\end{aligned}$$可得到Logistic回归算法，故Logistic分布属于指数分布族，得证。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 习题6.2\n",
    "&emsp;&emsp;写出Logistic回归模型学习的梯度下降算法。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**解答：**  \n",
    "对于Logistic模型：$$P(Y=1 | x)=\\frac{\\exp (w \\cdot x+b)}{1+\\exp (w \\cdot x+b)} \\\\ P(Y=0 | x)=\\frac{1}{1+\\exp (w \\cdot x+b)}\n",
    "$$对数似然函数为：$\\displaystyle L(w)=\\sum_{i=1}^N \\left[y_i (w \\cdot x_i)-\\log \\left(1+\\exp (w \\cdot x_i)\\right)\\right]$  \n",
    "似然函数求偏导，可得$\\displaystyle \\frac{\\partial L(w)}{\\partial w^{(j)}}=\\sum_{i=1}^N\\left[x_i^{(j)} \\cdot y_i-\\frac{\\exp (w \\cdot x_i) \\cdot x_i^{(j)}}{1+\\exp (w \\cdot x_i)}\\right]$  \n",
    "梯度函数为：$\\displaystyle \\nabla L(w)=\\left[\\frac{\\partial L(w)}{\\partial w^{(0)}}, \\cdots, \\frac{\\partial L(w)}{\\partial w^{(m)}}\\right]$  \n",
    "Logistic回归模型学习的梯度下降算法：  \n",
    "(1) 取初始值$x^{(0)} \\in R$，置$k=0$  \n",
    "(2) 计算$f(x^{(k)})$  \n",
    "(3) 计算梯度$g_k=g(x^{(k)})$，当$\\|g_k\\| < \\varepsilon$时，停止迭代，令$x^* = x^{(k)}$；否则，求$\\lambda_k$，使得$\\displaystyle f(x^{(k)}+\\lambda_k g_k) = \\max_{\\lambda \\geqslant 0}f(x^{(k)}+\\lambda g_k)$  \n",
    "(4) 置$x^{(k+1)}=x^{(k)}+\\lambda_k g_k$，计算$f(x^{(k+1)})$，当$\\|f(x^{(k+1)}) - f(x^{(k)})\\| < \\varepsilon$或 $\\|x^{(k+1)} - x^{(k)}\\| < \\varepsilon$时，停止迭代，令$x^* = x^{(k+1)}$  \n",
    "(5) 否则，置$k=k+1$，转(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from pylab import mpl\n",
    "\n",
    "# 图像显示中文\n",
    "mpl.rcParams['font.sans-serif'] = ['Microsoft YaHei']\n",
    "\n",
    "\n",
    "class LogisticRegression:\n",
    "    def __init__(self, learn_rate=0.1, max_iter=10000, tol=1e-2):\n",
    "        self.learn_rate = learn_rate  # 学习率\n",
    "        self.max_iter = max_iter  # 迭代次数\n",
    "        self.tol = tol  # 迭代停止阈值\n",
    "        self.w = None  # 权重\n",
    "\n",
    "    def preprocessing(self, X):\n",
    "        \"\"\"将原始X末尾加上一列，该列数值全部为1\"\"\"\n",
    "        row = X.shape[0]\n",
    "        y = np.ones(row).reshape(row, 1)\n",
    "        X_prepro = np.hstack((X, y))\n",
    "        return X_prepro\n",
    "\n",
    "    def sigmod(self, x):\n",
    "        return 1 / (1 + np.exp(-x))\n",
    "\n",
    "    def fit(self, X_train, y_train):\n",
    "        X = self.preprocessing(X_train)\n",
    "        y = y_train.T\n",
    "        # 初始化权重w\n",
    "        self.w = np.array([[0] * X.shape[1]], dtype=np.float)\n",
    "        k = 0\n",
    "        for loop in range(self.max_iter):\n",
    "            # 计算梯度\n",
    "            z = np.dot(X, self.w.T)\n",
    "            grad = X * (y - self.sigmod(z))\n",
    "            grad = grad.sum(axis=0)\n",
    "            # 利用梯度的绝对值作为迭代中止的条件\n",
    "            if (np.abs(grad) <= self.tol).all():\n",
    "                break\n",
    "            else:\n",
    "                # 更新权重w 梯度上升——求极大值\n",
    "                self.w += self.learn_rate * grad\n",
    "                k += 1\n",
    "        print(\"迭代次数：{}次\".format(k))\n",
    "        print(\"最终梯度：{}\".format(grad))\n",
    "        print(\"最终权重：{}\".format(self.w[0]))\n",
    "\n",
    "    def predict(self, x):\n",
    "        p = self.sigmod(np.dot(self.preprocessing(x), self.w.T))\n",
    "        print(\"Y=1的概率被估计为：{:.2%}\".format(p[0][0]))  # 调用score时，注释掉\n",
    "        p[np.where(p > 0.5)] = 1\n",
    "        p[np.where(p < 0.5)] = 0\n",
    "        return p\n",
    "\n",
    "    def score(self, X, y):\n",
    "        y_c = self.predict(X)\n",
    "        error_rate = np.sum(np.abs(y_c - y.T)) / y_c.shape[0]\n",
    "        return 1 - error_rate\n",
    "\n",
    "    def draw(self, X, y):\n",
    "        # 分离正负实例点\n",
    "        y = y[0]\n",
    "        X_po = X[np.where(y == 1)]\n",
    "        X_ne = X[np.where(y == 0)]\n",
    "        # 绘制数据集散点图\n",
    "        ax = plt.axes(projection='3d')\n",
    "        x_1 = X_po[0, :]\n",
    "        y_1 = X_po[1, :]\n",
    "        z_1 = X_po[2, :]\n",
    "        x_2 = X_ne[0, :]\n",
    "        y_2 = X_ne[1, :]\n",
    "        z_2 = X_ne[2, :]\n",
    "        ax.scatter(x_1, y_1, z_1, c=\"r\", label=\"正实例\")\n",
    "        ax.scatter(x_2, y_2, z_2, c=\"b\", label=\"负实例\")\n",
    "        ax.legend(loc='best')\n",
    "        # 绘制p=0.5的区分平面\n",
    "        x = np.linspace(-3, 3, 3)\n",
    "        y = np.linspace(-3, 3, 3)\n",
    "        x_3, y_3 = np.meshgrid(x, y)\n",
    "        a, b, c, d = self.w[0]\n",
    "        z_3 = -(a * x_3 + b * y_3 + d) / c\n",
    "        ax.plot_surface(x_3, y_3, z_3, alpha=0.5)  # 调节透明度\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "迭代次数：3232次\n",
      "最终梯度：[ 0.00144779  0.00046133  0.00490279 -0.00999848]\n",
      "最终权重：[  2.96908597   1.60115396   5.04477438 -13.43744079]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 训练数据集\n",
    "X_train = np.array([[3, 3, 3], [4, 3, 2], [2, 1, 2], [1, 1, 1], [-1, 0, 1],\n",
    "                    [2, -2, 1]])\n",
    "y_train = np.array([[1, 1, 1, 0, 0, 0]])\n",
    "# 构建实例，进行训练\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X_train, y_train)\n",
    "clf.draw(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 习题6.3\n",
    "&emsp;&emsp;写出最大熵模型学习的DFP算法。（关于一般的DFP算法参见附录B）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**解答：**  \n",
    "**第1步：**  \n",
    "最大熵模型为：$$\n",
    "\\begin{array}{cl}\n",
    "{\\max } & {H(p)=-\\sum_{x, y} P(x) P(y | x) \\log P(y | x)} \\\\ \n",
    "{\\text {st.}} &\n",
    "{E_p(f_i)-E_{\\hat{p}}(f_i)=0, \\quad i=1,2, \\cdots,n} \\\\ \n",
    "& {\\sum_y P(y | x)=1}\n",
    "\\end{array}$$引入拉格朗日乘子，定义拉格朗日函数：$$\n",
    "L(P, w)=\\sum_{xy} P(x) P(y | x) \\log P(y | x)+w_0 \\left(1-\\sum_y P(y | x)\\right) \\\\\n",
    "+\\sum_{i=1} w_i\\left(\\sum_{xy} P(x, y) f_i(x, y)-\\sum_{xy} P(x, y) P(y | x) f_i(x, y)\\right)$$\n",
    "最优化原始问题为：$$\\min_{P \\in C} \\max_{w} L(P,w)$$对偶问题为：$$\\max_{w} \\min_{P \\in C} L(P,w)$$令$$\\Psi(w) = \\min_{P \\in C} L(P,w) = L(P_w, w)$$$\\Psi(w)$称为对偶函数，同时，其解记作$$P_w = \\mathop{\\arg \\min}_{P \\in C} L(P,w) = P_w(y|x)$$求$L(P,w)$对$P(y|x)$的偏导数，并令偏导数等于0，解得：$$P_w(y | x)=\\frac{1}{Z_w(x)} \\exp \\left(\\sum_{i=1}^n w_i f_i (x, y)\\right)$$其中：$$Z_w(x)=\\sum_y \\exp \\left(\\sum_{i=1}^n w_i f_i(x, y)\\right)$$则最大熵模型目标函数表示为$$\\varphi(w)=\\min_{w \\in R_n} \\Psi(w) = \\sum_{x} P(x) \\log \\sum_{y} \\exp \\left(\\sum_{i=1}^{n} w_{i} f_{i}(x, y)\\right)-\\sum_{x, y} P(x, y) \\sum_{i=1}^{n} w_{i} f_{i}(x, y)$$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**第2步：**  \n",
    "DFP的$G_{k+1}$的迭代公式为：$$G_{k+1}=G_k+\\frac{\\delta_k \\delta_k^T}{\\delta_k^T y_k}-\\frac{G_k y_k y_k^T G_k}{y_k^T G_k y_k}$$  \n",
    "**最大熵模型的DFP算法：**   \n",
    "输入：目标函数$\\varphi(w)$，梯度$g(w) = \\nabla g(w)$，精度要求$\\varepsilon$；  \n",
    "输出：$\\varphi(w)$的极小值点$w^*$  \n",
    "(1)选定初始点$w^{(0)}$，取$G_0$为正定对称矩阵，置$k=0$  \n",
    "(2)计算$g_k=g(w^{(k)})$，若$\\|g_k\\| < \\varepsilon$，则停止计算，得近似解$w^*=w^{(k)}$，否则转(3)  \n",
    "(3)置$p_k=-G_kg_k$  \n",
    "(4)一维搜索：求$\\lambda_k$使得$$\\varphi\\left(w^{(k)}+\\lambda_k P_k\\right)=\\min _{\\lambda \\geqslant 0} \\varphi\\left(w^{(k)}+\\lambda P_{k}\\right)$$(5)置$w^{(k+1)}=w^{(k)}+\\lambda_k p_k$  \n",
    "(6)计算$g_{k+1}=g(w^{(k+1)})$，若$\\|g_{k+1}\\| < \\varepsilon$，则停止计算，得近似解$w^*=w^{(k+1)}$；否则，按照迭代式算出$G_{k+1}$  \n",
    "(7)置$k=k+1$，转(3)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "参考代码：https://github.com/wzyonggege/statistical-learning-method\n",
    "\n",
    "本文代码更新地址：https://github.com/fengdu78/lihang-code\n",
    "\n",
    "习题解答：https://github.com/datawhalechina/statistical-learning-method-solutions-manual\n",
    "\n",
    "中文注释制作：机器学习初学者公众号：ID:ai-start-com\n",
    "\n",
    "配置环境：python 3.5+\n",
    "\n",
    "代码全部测试通过。\n",
    "![gongzhong](../gongzhong.jpg)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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